Work, energy and power: follow transfers and rates

1. A force does work through displacement

For a constant force along a straight displacement, work is W = Fs, where F is force in newtons and s is displacement in metres. The unit is the joule (J), equal to one newton metre. More generally, use only the force component along the displacement. A force in the same direction does positive work; an opposing force does negative work; a perpendicular force does zero work in this model. A person holding a bag motionless exerts a force, but that supporting force does no mechanical work on the stationary bag. The person’s muscles can still use chemical energy, so everyday effort and this specific physics definition are different.

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2. Net work changes kinetic energy

Translational kinetic energy is K = ½mv², where m is mass in kilograms and v is speed in metres per second. K is in joules and is never negative, even if velocity points in the chosen negative direction. For a constant-mass particle, the work done by the net force equals the change in kinetic energy, W_net = K_final − K_initial. Work by one force alone is not automatically the total. If speed doubles, kinetic energy becomes four times as large because speed is squared. This relationship explains why stopping distance can increase strongly with speed, but a prediction still requires a model of the stopping force and conditions.

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3. Potential energy belongs to an interaction

Near Earth’s surface, changing an object’s height by Δh changes gravitational potential energy by ΔU = mgΔh. Here g is gravitational acceleration, and the approximation assumes it is nearly constant over the height range. We often write U = mgh after choosing a zero height. A different zero changes the quoted U but not the difference between two positions. Strictly this energy belongs to the Earth–object interaction, rather than being an ingredient hidden inside the object. When the object falls, decreasing gravitational potential energy can become kinetic energy. A stretched spring provides another form of potential energy associated with its deformation, showing that position and configuration matter as well as speed.

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4. Choose which forms and transfers to include

Mechanical energy is the sum of kinetic and relevant potential energies. It remains constant in a suitable isolated model with only conservative interactions, such as ideal gravitational motion without air resistance. With friction, mechanical energy can become internal energy of contacting materials, sound or deformation. Total energy is conserved when all forms and transfers are accounted for, even when mechanical energy decreases. A system boundary keeps the explanation honest: energy supplied by a motor or carried away to surroundings must appear in the accounting. Saying energy was “used up” usually means it became less useful for the chosen task, not that it vanished from the universe.

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5. Power compares the same transfer with time

Average power is P = E/t for an energy transfer E over time t, or work divided by time. Its unit is watt (W), where 1 W = 1 J/s. The letter W can therefore mean work in an equation or watt as a unit; the context distinguishes them. A kilowatt is 1000 watts. A kilowatt-hour is energy, not power: it is the transfer produced by 1 kW acting for 1 hour. Efficiency compares useful output energy with input energy, multiplied by 100%. “Useful” depends on the stated purpose. The remaining energy still exists, perhaps as unwanted warming or sound. Higher power does not automatically mean higher efficiency.

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6. Worked example: books moved to a library shelf

Illustrative model: a 12 kg box of books is raised vertically by 1.5 m in 6 s. Use g = 10 m/s² and assume equal starting and ending speeds, with negligible losses. Increase in gravitational potential energy is 12 × 10 × 1.5 = 180 J. The lifting agent supplies 180 J of work, while gravity does −180 J; their net work is zero because kinetic energy has no final change. Average useful lifting power is 180/6 = 30 W. Completing the same ideal lift in 3 s requires 60 W average useful power but still 180 J. Actual human energy expenditure need not equal this mechanical output.

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7. Worked example: speed squared changes the distance

Illustrative straight-line cart model: mass 20 kg, initial speed 3 m/s and a constant opposing force of 9 N on a level surface. Initial kinetic energy is ½ × 20 × 3² = 90 J. To stop, net work must be −90 J. Since the opposing force does work −9s, the stopping distance is s = 90/9 = 10 m. At twice the initial speed, 6 m/s, kinetic energy becomes 360 J and stopping distance becomes 40 m under the same force assumption. This fourfold result depends on that model; varying braking force, a slope or extra energy transfers would change the prediction.

Sources: NCERT: Work, Energy and Power ↗

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